Problem: What do the following two equations represent? $x+3y = -4$ $-4x-12y = 16$
Solution: Putting the first equation in $y = mx + b$ form gives: $x+3y = -4$ $3y = -x-4$ $y = -\dfrac{1}{3}x - \dfrac{4}{3}$ Putting the second equation in $y = mx + b$ form gives: $-4x-12y = 16$ $-12y = 4x+16$ $y = -\dfrac{1}{3}x - \dfrac{4}{3}$ The above equations turn into the same equation, so they represent equal lines.